For non-Hermitian Hamiltonians, the Arnoldi diagonal and subdiagonal coefficients are the Flaschka variables of the finite two-dimensional Toda lattice, and their squares give both the Fubini-Study metric and the Berry curvature of the Krylov subspaces.
The condition prevents Arnoldi breakdown forn < N−1and yields a complete unitary transfor- mation [9, 10]
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Two-dimensional Toda--Arnoldi correspondence: Holomorphic Krylov geometry and counterdiabatic transport
For non-Hermitian Hamiltonians, the Arnoldi diagonal and subdiagonal coefficients are the Flaschka variables of the finite two-dimensional Toda lattice, and their squares give both the Fubini-Study metric and the Berry curvature of the Krylov subspaces.